Finite Group Databasebeta

← D5×#4877 #14430198

Subgroups — D5×#4877 #14430198

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#890C211yesmaximal, characteristic
2D5×#887C211yesmaximal, characteristic
3#11750978C211yesmaximal, characteristic, complemented
4C5×#4877C211yesmaximal, characteristic, complemented
5C3×D5×#107C211yesmaximal, characteristic
6#11747887C211yesmaximal, characteristic, complemented
7#11747874C211yesmaximal, characteristic, complemented
8D5×#816C211yesmaximal, characteristic
9D5×Dic3⋊C8C211yesmaximal, characteristic
10D5×#810C211yesmaximal, characteristic
11D5×#808C211yesmaximal, characteristic
12#11747393C211yesmaximal, characteristic, complemented
13#11747298C211yesmaximal, characteristic, complemented
14#11747290C211yesmaximal, characteristic, complemented
15#11747184C211yesmaximal, characteristic, complemented
16D5×#479—31nomaximal, Hall
17C2×D5×Dic6C2211yescharacteristic
18#91779C2211yescharacteristic
19#91776C2211yescharacteristic
20C5×#890C2211yescharacteristic
21C5×#887C2211yescharacteristic
22C2×C3×C8×D5C2211yescharacteristic
23C3×D5×C4⋊C4C2211yescharacteristic
24C3×D5×C4⋊C4C2211yescharacteristic
25D5×C4⋊Dic3—21no—
26D5×C4⋊Dic3C2211yescharacteristic
27D5×Dic3⋊C4—21no—
28D5×Dic3⋊C4—21no—
29C4×D5×Dic3—21no—
30C4×D5×Dic3C2211yescharacteristic
31#91384C2211yescharacteristic
32#91381C2211yescharacteristic
33#91344C2211yescharacteristic
34#91340C2211yescharacteristic
35#91335—21no—
36#91334—21no—
37#91325—21no—
38#91324—21no—
39C2×D5×C3⋊C8C2211yescharacteristic
40C3×C5×#107C2211yescharacteristic
41#91100C2211yescharacteristic
42#91098C2211yescharacteristic
43#91094C2211yescharacteristic
44#91092C2211yescharacteristic
45C5×#816C2211yescharacteristic
46C5×Dic3⋊C8C2211yescharacteristic
47C5×#810C2211yescharacteristic
48C5×#808C2211yescharacteristic
49C3×#3950C2211yescharacteristic
50C3×#3939C2211yescharacteristic
51C3×#3939C2211yescharacteristic
52#90987C2211yescharacteristic
53#90986C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55#90983C2211yescharacteristic
56#90975C2211yescharacteristic
57#90974C2211yescharacteristic
58#90973C2211yescharacteristic
59#90972C2211yescharacteristic
60C2×#4877—51nomaximal, Hall
61D5×#125—31no—
62C4×Q8×D5—31no—
63C5×#479—31no—
64#65352—31no—
65#65311—31no—
66D5×#107D311yescharacteristic
67#65166—31no—
68D5×#106—31no—
69#65146—31no—
70D5×C4⋊C8—31no—
71#65118—31no—
72D5×#103—31no—
73D5×#103—31no—
74#65088—31no—
75#65085—31no—
76C2×Dic30C2311yescharacteristic
77C2×C5×Dic6C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×C4×D5—21no—
80C2×C3×C4×D5C2311yescharacteristic
81C2×#1204—21no—
82C2×D5×Dic3—21no—
83C2×D5×Dic3—21no—
84C2×D5×Dic3D411yescharacteristic
85C2×D5×Dic3D411yescharacteristic
86D5×Dic6—22no—
87D5×Dic6Q814yes—
88C2×C3×C5×C8C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91C4⋊Dic15—21no—
92C4⋊Dic15C2311yescharacteristic
93#6712—21no—
94#6712—21no—
95C4×Dic15—21no—
96C4×Dic15C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×C4⋊Dic3—21no—
99C5×C4⋊Dic3C2311yescharacteristic
100C5×Dic3⋊C4—21no—
101C5×Dic3⋊C4—21no—
102C4×C5×Dic3—21no—
103C4×C5×Dic3C2311yescharacteristic
104C2×C5×C3⋊C8C2311yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C2×C3×#168C2311yescharacteristic
110C3×C8×D5—22no—
111Dic3⋊Dic5—21no—
112Dic3⋊Dic5—21no—
113#6669—21no—
114#6669—21no—
115#6668—21no—
116#6668—21no—
117#6668—21no—
118Dic3×Dic5—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5D411yescharacteristic
121Dic3×Dic5D411yescharacteristic
122D5×C3⋊C8—22no—
123C2×#890—51no—
124C2×#887—51no—
125C2×C3×#107—51no—
126C2×#816—51no—
127C2×Dic3⋊C8—51no—
128C2×#810—51no—
129C2×#808—51no—
130#4877—51no—
131#4877—51no—
132#4877—51no—
133#4877—51no—
134#4877—51no—
135#4877—51no—
136#4877—51no—
137#4877D511yescharacteristic, direct product factor
138C2×Q8×D5—31no—
139C5×#125—31no—
140C4×C5×Q8—31no—
141Q8×Dic5—31no—
142C2×C8×D5—31no—
143C2×C8×D5C2×D311yescharacteristic
144D5×C4⋊C4—31no—
145D5×C4⋊C4—61no—
146D5×C4⋊C4—61no—
147D5×C4⋊C4—61no—
148D5×C4⋊C4C2×D311yescharacteristic
149D5×C4⋊C4C2×D311yescharacteristic
150#4036—31no—
151#4036—31no—
152#4035—61no—
153#4035—61no—
154#4033—31no—
155#4033—61no—
156C42×D5—31no—
157C42×D5—61no—
158#4016—31no—
159C4×Dic10—31no—
160C4×Dic10—61no—
161C5×#107C2×D311yescharacteristic
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#103—31no—
165C5×#103—31no—
166#3967—31no—
167#3967—31no—
168#3950C2×D311yescharacteristic
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3940—31no—
178#3939C2×D311yescharacteristic
179#3939C2×D311yescharacteristic
180C4⋊#168—31no—
181C2×#479—151noSylow
182C22×C3×D5C2×D411yescharacteristic
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C2411yescharacteristic
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15C2×D411yescharacteristic
189C2×Dic15C2×D411yescharacteristic
190Dic30—21no—
191Dic30C2×Q812yes—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3C2×D411yescharacteristic
195C2×C5×Dic3C2×D411yescharacteristic
196C5×Dic6—21no—
197C5×Dic6C2×Q812yes—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5C2×D411yescharacteristic
201C3×C4×D5—42no—
202C3×C4×D5—42no—
203C3×C4×D5C2×Q812yes—
204C3×C4×D5#4112yes—
205#1204—24no—
206D5×Dic3—24no—
207D5×Dic3—22no—
208D5×Dic3—22no—
209D5×Dic3—42no—
210C3×C5×C8—21no—
211C3⋊#168—21no—
212C3×#168—21no—
213C5×C3⋊C8—21no—
214C22×Dic6—51no—
215C22×C3×C8—51no—
216C2×C3×C4⋊C4—51no—
217C2×C3×C4⋊C4—51no—
218C2×C4⋊Dic3—51no—
219C2×C4⋊Dic3—101no—
220C2×Dic3⋊C4—101no—
221C2×Dic3⋊C4—101no—
222C2×C4×Dic3—51no—
223C2×C4×Dic3—101no—
224C22×C3⋊C8—51no—
225#890—51no—
226#890—51no—
227#890—51no—
228#890—101no—
229#890—101no—
230#890C2×D511yescharacteristic
231#887—51no—
232#887—51no—
233#887—51no—
234#887—101no—
235#887—101no—
236#887C2×D511yescharacteristic
237C3×#107—51no—
238C3×#107—51no—
239C3×#107—51no—
240C3×#107C2×D511yescharacteristic
241#816—51no—
242#816—51no—
243#816—51no—
244#816C2×D511yescharacteristic
245Dic3⋊C8—51no—
246Dic3⋊C8—51no—
247Dic3⋊C8—51no—
248Dic3⋊C8C2×D511yescharacteristic
249#810—51no—
250#810—51no—
251#810—51no—
252#810C2×D511yescharacteristic
253#808—51no—
254#808—51no—
255#808—51no—
256#808C2×D511yescharacteristic
257C2×C5×Q8—31no—
258Q8×D5—34no—
259Q8×D5—62no—
260C2×C4×D5—21no—
261C2×C4×D5—21no—
262C2×C4×D5—31no—
263C2×C4×D5—31no—
264C2×C4×D5—61no—
265C2×C4×D5—61no—
266C2×C4×D5C22×D311yescharacteristic
267C2×Dic10—31no—
268C2×Dic10—61no—
269C2×C5×C8—31no—
270C2×C5×C8C22×D311yescharacteristic
271C5×C4⋊C4—31no—
272C5×C4⋊C4—61no—
273C5×C4⋊C4—61no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4C22×D311yescharacteristic
276C5×C4⋊C4C22×D311yescharacteristic
277C42×C5—31no—
278C42×C5—61no—
279C4⋊Dic5—31no—
280C4⋊Dic5—61no—
281C4⋊Dic5—61no—
282C4⋊Dic5—61no—
283C4⋊Dic5C22×D311yescharacteristic
284C4⋊Dic5C22×D311yescharacteristic
285#683—21no—
286#683—21no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293#683—61no—
294C4×Dic5—31no—
295C4×Dic5—31no—
296C4×Dic5—31no—
297C4×Dic5—61no—
298C4×Dic5—61no—
299C4×Dic5—61no—
300C2×#168—31no—
301C2×#168C22×D311yescharacteristic
302C8×D5—22no—
303C8×D5—62no—
304C2×#125—151no—
305C2×C4×Q8—151no—
306#479—31no—
307#479—151no—
308#479—151no—
309#479—151no—
310#479—151no—
311#479—151no—
312#479—151no—
313#479—151no—
314C2×#107—51no—
315C2×#106—151no—
316C2×C4⋊C8—151no—
317C2×#103—151no—
318C2×#103—151no—
319C22×C3×C5C22×D411yescharacteristic
320C2×C3×D5C22⋊Q812yes—
321C2×C3×D5#13512yes—
322C2×C3×D5#13712yes—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×C4×C5C22×Q811yescharacteristic
326C3×C4×C5C2×#4111yescharacteristic
327Dic15—22no—
328Dic15—21no—
329Dic15—21no—
330Dic15—41no—
331C3×Dic5—41no—
332C3×Dic5—41no—
333C3×Dic5C22⋊Q812yes—
334C5×Dic3—22no—
335C5×Dic3—21no—
336C5×Dic3—21no—
337C5×Dic3—41no—
338C22×C3×C4—51no—
339C22×C3×C4—101no—
340C22×C3×C4—101no—
341C22×Dic3—51no—
342C22×Dic3—51no—
343C22×Dic3—101no—
344C22×Dic3—101no—
345C2×Dic6—51no—
346C2×Dic6—54no—
347C2×Dic6—102no—
348C2×Dic6—101no—
349C2×Dic6C22×D511yescharacteristic
350C2×C3×C8—51no—
351C2×C3×C8—102no—
352C2×C3×C8C22×D511yescharacteristic
353C3×C4⋊C4—51no—
354C3×C4⋊C4—51no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4—101no—
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C4⋊C4C22×D511yescharacteristic
359C4⋊Dic3—21no—
360C4⋊Dic3—51no—
361C4⋊Dic3—101no—
362C4⋊Dic3—101no—
363C4⋊Dic3—101no—
364C4⋊Dic3—101no—
365C4⋊Dic3C22×D511yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374C4×Dic3—21no—
375C4×Dic3—51no—
376C4×Dic3—51no—
377C4×Dic3—51no—
378C4×Dic3—101no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C4×Dic3C22×D511yescharacteristic
382C2×C3⋊C8—51no—
383C2×C3⋊C8—102no—
384C2×C3⋊C8C22×D511yescharacteristic
385C22×D5D3×D411yescharacteristic
386C5×Q8—32no—
387C5×Q8—61no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—31no—
391C2×C4×C5—31no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5C23×D311yescharacteristic
395C2×Dic5—21no—
396C2×Dic5—21no—
397C2×Dic5—31no—
398C2×Dic5—31no—
399C2×Dic5—61no—
400C2×Dic5—61no—
401C2×Dic5D3×D411yescharacteristic
402C4×D5—42no—
403C4×D5—42no—
404C4×D5—64no—
405C4×D5—62no—
406C4×D5—62no—
407C4×D5—122no—
408C4×D5#23512yes—
409C4×D5D3×Q812yes—
410Dic10—32no—
411Dic10—61no—
412Dic10—64no—
413C5×C8—21no—
414C5×C8—61no—
415#168—21no—
416#168—61no—
417C22×Q8—151no—
418C22×C8—51no—
419C22×C8—151no—
420#125—31no—
421#125—151no—
422#125—151no—
423#125—151no—
424#125—301no—
425#125—301no—
426C4×Q8—31no—
427C4×Q8—151no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8—301no—
431C4×Q8—301no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—301no—
436C2×C4⋊C4—301no—
437C2×C4⋊C4—301no—
438C2×C42—151no—
439C2×C42—301no—
440#107—51no—
441#107—51no—
442#107—51no—
443#107D3×D511yescharacteristic
444#106—31no—
445#106—151no—
446#106—151no—
447#106—151no—
448C4⋊C8—31no—
449C4⋊C8—151no—
450C4⋊C8—151no—
451C4⋊C8—151no—
452#103—31no—
453#103—31no—
454#103—151no—
455#103—151no—
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460C2×C3×C5C2×C22⋊Q811yescharacteristic
461C2×C3×C5C2×#13511yescharacteristic
462C2×C3×C5C2×#13711yescharacteristic
463C3×D5#47914yescomplemented
464C23×C3—51no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—51no—
468C2×C3×C4—52no—
469C2×C3×C4—52no—
470C2×C3×C4—101no—
471C2×C3×C4—101no—
472C2×C3×C4—202no—
473C2×C3×C4—202no—
474C2×C3×C4C23×D511yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—51no—
478C2×Dic3—51no—
479C2×Dic3—104no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—101no—
483C2×Dic3—101no—
484C2×Dic3—202no—
485C2×Dic3D4×D511yescharacteristic
486C2×Dic3D4×D511yescharacteristic
487Dic6—21no—
488Dic6—52no—
489Dic6—104no—
490Dic6—101no—
491Dic6Q8×D512yes—
492C3×C8—21no—
493C3×C8—101no—
494C3⋊C8—21no—
495C3⋊C8—101no—
496C22×C5C2×D3×D411yescharacteristic
497C2×D5#89612yes—
498C2×D5#91212yes—
499C2×D5#91812yes—
500C4×C5—41no—
501C4×C5—41no—
502C4×C5—61no—
503C4×C5—62no—
504C4×C5—61no—
505C4×C5—121no—
506C4×C5C2×#23511yescharacteristic
507C4×C5C2×D3×Q811yescharacteristic
508Dic5—41no—
509Dic5—41no—
510Dic5—61no—
511Dic5—62no—
512Dic5—61no—
513Dic5—121no—
514Dic5#89612yes—
515C2×Q8—31no—
516C2×Q8—154no—
517C2×Q8—151no—
518C2×Q8—301no—
519C2×Q8—302no—
520C22×C4—51no—
521C22×C4—101no—
522C22×C4—101no—
523C22×C4—151no—
524C22×C4—151no—
525C22×C4—301no—
526C22×C4—301no—
527C2×C8—31no—
528C2×C8—51no—
529C2×C8—102no—
530C2×C8—151no—
531C2×C8—302no—
532C2×C8C2×D3×D511yescharacteristic
533C4⋊C4—31no—
534C4⋊C4—51no—
535C4⋊C4—51no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—101no—
540C4⋊C4—101no—
541C4⋊C4—151no—
542C4⋊C4—301no—
543C4⋊C4—301no—
544C4⋊C4—301no—
545C4⋊C4—301no—
546C4⋊C4—301no—
547C4⋊C4—301no—
548C4⋊C4—301no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4C2×D3×D511yescharacteristic
553C4⋊C4C2×D3×D511yescharacteristic
554C42—31no—
555C42—61no—
556C42—151no—
557C42—151no—
558C42—151no—
559C42—301no—
560C42—301no—
561C42—301no—
562C3×C5C2×#47911yescharacteristic, complemented, Hall
563C22×C3—52no—
564C22×C3—52no—
565C22×C3—52no—
566C22×C3C2×D4×D511yescharacteristic
567C3×C4—41no—
568C3×C4—41no—
569C3×C4—52no—
570C3×C4—201no—
571C3×C4—201no—
572C3×C4C2×Q8×D511yescharacteristic
573C3×C4D5×#4111yescharacteristic
574Dic3—21no—
575Dic3—21no—
576Dic3—22no—
577Dic3—41no—
578Dic3—101no—
579Dic3—101no—
580Dic3—102no—
581Dic3—201no—
582C2×C5C2×#89611yescharacteristic
583C2×C5C2×#91211yescharacteristic
584C2×C5C2×#91811yescharacteristic
585D5#487714yesdirect product factor
586C23—51no—
587Q8—32no—
588Q8—61no—
589Q8—152no—
590Q8—304no—
591Q8—301no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—51no—
597C2×C4—52no—
598C2×C4—52no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—101no—
602C2×C4—101no—
603C2×C4—151no—
604C2×C4—151no—
605C2×C4—202no—
606C2×C4—202no—
607C2×C4—302no—
608C2×C4—302no—
609C2×C4—304no—
610C2×C4—301no—
611C2×C4—301no—
612C2×C4—602no—
613C2×C4C22×D3×D511yescharacteristic
614C8—21no—
615C8—61no—
616C8—101no—
617C8—301no—
618C2×C3—54no—
619C2×C3D5×C22⋊Q811yescharacteristic
620C2×C3D5×#13511yescharacteristic
621C2×C3D5×#13711yescharacteristic
622C5C2×#487711yescharacteristic, complemented, Sylow
623C22—52no—
624C22—52no—
625C22—52no—
626C22D3×D4×D511yescharacteristic
627C4—41no—
628C4—41no—
629C4—52no—
630C4—61no—
631C4—61no—
632C4—62no—
633C4—121no—
634C4—201no—
635C4—201no—
636C4—301no—
637C4—301no—
638C4—302no—
639C4—601no—
640C4D5×#23511yescharacteristic
641C4D3×Q8×D511yescharacteristic
642C3D5×#47911yescharacteristic, complemented, Sylow
643C2—54no—
644C2D5×#89611yescharacteristic
645C2D5×#91211yescharacteristic
646C2D5×#91811yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenter#107D3×D5
hypocenterC3×C5C2×#479
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #11750978C2semidirect
4. C5×#4877C2semidirect
6. #11747887C2semidirect
7. #11747874C2semidirect
12. #11747393C2semidirect
13. #11747298C2semidirect
14. #11747290C2semidirect
15. #11747184C2semidirect
137. #4877D5direct (N × H)
463. C3×D5#479semidirect
562. C3×C5C2×#479semidirect
585. D5#4877direct (N × H)
622. C5C2×#4877semidirect
642. C3D5×#479semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D5×#8902
D5×#8872
#117509782
C5×#48772
C3×D5×#1072
#117478872
#117478742
D5×#8162
D5×Dic3⋊C82
D5×#8102
D5×#8082
#117473932
#117472982
#117472902
#117471842
D5×#4793
C2×#48775